Subversion Repositories wimsdev

!goto $wims_read_parm

:def

title=Implicit derivative

synonyme=implicit function differentiation, differentiate implicitly, derivative of implicit function

input=equation

!exit

:proc

formula=!item 1 of $formula

t=!varlist nofn $formula

t=!listintersect $t and p,q,r,s,t,u,v,w,x,y,z,P,Q,R,S,T,U,V,W,X,Y,Z

t=!sort nocase item $t

vcnt=!itemcnt $t

!if $vcnt<2

 error=bad_formula

 !exit

!endif

eq==

!if $eq isin $formula

 fml=!translate $eq to , in $formula

 !distribute items $fml into f1, f2

 !if $f2=$empty

  error=bad_formula

  !exit

 !endif

 fml=$f1 - ($f2)

!else

 fml=$formula

 formula=$formula = 0

!endif

variable=!items2words $variable

x=!word 1 of $variable

!if $x=$empty

 x=!item 1 of $t

!endif

remain=!listcomplement $x in $t

maxima_header=f:$fml;dx:diff(f,$x,1);

msrc=

!for i in $remain

 msrc=!append line -dx/diff(f,$i,1); to $msrc

!next i

result=!exec maxima $msrc

!exit

:output

Derivative of the implicit function

!htmlmath $formula

 with respect to $x:

<p><center>

!for i=1 to $vcnt-1

 !set v=!item $i of $remain

 !set q=!line $i of $result

 !if $q!=$empty

  !if $vcnt<=2

   <p>d$v/d$x =

  !else

   <p>$m_partial$v/$m_partial$x =

  !endif

  !htmlmath $q

 !endif

!next i

</center> <p>

!exit